A new and distinct pistachio tree named `PETE I`, characterized by a very white shell nut with a 90% or higher split ratio and a large nut size (18 to 20 nuts per ounce), nut meat color brilliant purple on the exterior with a dark green interior, a very high resistance to Botryosphaeria panicle and shoot blight (Botryosphaeria dothidea) fungus, large, dark green leaves and an early bloom.